Lenses alter the direction of travel of transmitted electromagnetic waves. Lenses are often used to focus or defocus beams or parallel rays of electromagnetic energy incident on a surface of the lens. Some everyday devices that use lenses include corrective eyeglasses, cameras, and binoculars. In these applications, the lenses focus electromagnetic energy radiating at optical frequencies. Lenses are also commonly used for high frequency electromagnetic radiation, such as microwave frequencies and frequencies extending into the gigahertz range.
One type of lens is a gradient lens. Typically, a gradient lens is a device for which the dielectric constant of the material from which the lens is constructed, and thus the index of refraction, varies along a path of a ray representing energy direction of propagation passes through the lens. As the ray passes from a first medium having a first index of refraction into a second medium having a different index of refraction at a direction that is not perpendicular to the boundary between the two mediums, the direction of the ray is changed. If the first medium has a smaller index of refraction than that of the second medium, the ray bends toward a normal perpendicular to the boundary as the ray passes into the second medium. That is, the ray in the second medium is propagating in a direction closer to the normal.
Most lenses focus incoming light to a focal point that is substantially removed from the lens. However, in many applications, it would be useful for the focal point(s) of a lens to be on a surface of the lens. Lenses with focal points on the surface of the lens include Luneburg lenses, Maxwell fisheye lenses and constant-K lenses. These lenses tend to be spheres which can be large and heavy as aperture size increases. Accordingly, a need in the art exists for a lens that can focus parallel rays of electromagnetic energy received at one surface of a lens onto a focal point at a second surface of the lens where the lens is smaller than a full sphere.